Neural networks Wavelet

The WNN is based on the similarity found between the inverse WT Stromberg s equation (Eq. 9.19) and a hidden layer in the Multi-Layer Perceptron (MLP) network structure (Meyer 1993). In fact, the wavelet decomposition can be seen like a neuronal network model, where the wavelets are indexed by i = instead of the double 

The compact system of functions located in the hidden layer allows MLPs with only three layers to approximate any arbitrary and continuous function (Hornik 1989, Scarselli 1998). The predetermined precision is defined by the characteristics of the family of functions used as well as by the approach error to reach. In the development of a WNN, a MLP structure with just three layers (input, hidden and output layer) is usually considered, because both the analysis and the implementation are simpler. 

Orthogonal wavelets are related with theory of multiresolution analysis and usually cannot be expressed in an informal context they must fulfill stringent orthogonal conditions, on the other hand, wavelet frames are constructed by simple operations of translation and dilation and are the easiest to use (Akay 1997, Heil 1989, Gutes et al. 

Although many wavelet applications use orthogonal wavelet basis, others work better with redundant wavelet families. The redundant representation offered by wavelet frames has demonstrated to be good both in signal denoising and compaction (Daubechies et al. 1986, 1992). 

In this way any desired signal / (x) can be approximated by generalizing a linear 

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Tabaraki, R., Khayamian, T. and Ensafi, A.A. (2006) Wavelet neural network modeling in QSPR for prediction of solubility of 25 anthraquinone dyes at different temperatures and pressures in supercritical carbon dioxide./. Md. Graph. Model., 25, 46-54. 

Spectral compression with wavelet neural network... 

Fig. 4 The architecture of (a) a. single iayer neurai network with the. sigmoidal transfer function, as well as the wavelet neural network for (h) IR spectral data compre.ssion. and (c) pattern recognition in ilV-VIS spectroscopy.

W. Liu, Y.M. Wang. Z.X. Pan. W.L. Zhou and M S. Zhang. Simultaneous Determination of Molybdenum and Tungsten using Wavelet Neural Network, Chinese Journal of Analytical Chemistry. 25 (1997). 1189-1191 (in Chinese). 

Multivariate Calibration Model for a Voltammetric Electronic Tongue Based on a Multiple Output Wavelet Neural Network... 

Guo, Q.X., Liu, L., Cai, W.S., Jiang, Y., Liu, Y.C. Driving force prediction for inclusion com-plexation of a-cyclodextrin with benzene derivatives by a wavelet neural network. Chem. Phys. Lett. 290, 514-518 (1998)... 

Gutes, A., Cespedes, F., Cartas, R., Alegret, S., del Valle, M., Gutierrez, J.M., Munoz, R. Multivariate calibration model from overlapping voltammetric signals employing wavelet neural networks. Chemometr. Intell. Lab. Syst. 83,169-179 (2006)... 

Iyengar, S.S., Cho, E.C., Phoha, V.V. Foundations of wavelet neural networks. Chapman Hall/CRC, Boca Raton (2002)... 

Khayamian, T., Ensafi, A.A., Benvidi, A. Extending the dynamic range of copper determination in differential pulse adsorption cathodic stripping voltammetry using wavelet neural network. Talanta 69, 1176-1181 (2006)... 

Zhang, J., Walter, G.G., Miao, Y., Lee, W.N.W. Wavelet neural networks for function learning. IEEE Trans. Signal Processing 43, 1485-1497 (1995)... 

Xue Pengqian, WU Lifeng, Li Haijun. Prediction of gas emission based on the wavelet neural network [J]. China Safety Science Journal, 2006,2. 

A second approach to data compression is to compress infrared spectra with a construct called a wavelet neural network (WNN). The WNN approach stores large amounts of infrared data for fast archiving of spectral data. It is achieved by modifying the machine learning technique of artificial neural networks (ANNs) to capture the shape of infrared spectra using wavelet basis functions. The WNN approach is similar to another approach... 

Q Introducing SPIDA-Web Wavelets, Neural Networks and InternetAccessibilityinan Image-Based Automated Identification System... 

Subasi, A, Yilmaz, M Ozcalik, HR. Classification of EMG signals using wavelet neural network. Journal of neuroscience methods 2006 156 360-367... 

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